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Let a and b be the solutions to 7x^2 + x - 5 = 0. What is the solution to (a - 4)(b - 4)?

 Mar 24, 2020
 #1
avatar+1970 
+1

Hint:

 

Factor the equation, then find the roots of it (a+#)(b+#) Then, do (a-4)(b-4)

 

Hope this helped!

 Mar 24, 2020
 #2
avatar+111330 
+1

(a - 4) (b - 4)  =  

 

(ab)^2 -  4(a +b)  +  16       (1)

 

 

By Vieta

 

The  sum of  the roots   a + b =  -1/7     (2)

 

And the product of the roots,  ab  =  -5/7 =  -5/7      (3)

 

Subbing   (2)  and (3) into (1)  we get that

 

(-5/7)^2  - 4(-1/7)  +  16  = 

 

25/49  + 4/7  + 16  =

 

[25  + 28 + 784 ] / 49 

 

837 / 49

 

 

cool cool cool

 Mar 24, 2020

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